Short texts pose significant challenges for clustering due to semantic sparsity, limited context, and fuzzy category boundaries. Although recent contrastive learning methods improve instance-level representation, they often overlook local semantic structure within the clustering head. Moreover, treating semantically similar neighbors as negatives impair cluster-level discrimination. To address these issues, we propose Fuzzy Neighborhood-Aware Self-Supervised Contrastive Clustering (FNSCC) framework. FNSCC incorporates neighborhood information at both the instance-level and cluster-level. At the instance-level, it excludes neighbors from the negative sample set to enhance inter-cluster separability. At the cluster-level, it introduces fuzzy neighborhood-aware weighting to refine soft assignment probabilities, encouraging alignment with semantically coherent clusters. Experiments on multiple benchmark short text datasets demonstrate that FNSCC consistently outperforms state-of-the-art models in accuracy and normalized mutual information. Our code is available at https://github.com/zjzone/FNSCC.